unbiased estimates of the fractions of variation. Remember also that adjusted R
2 can
be negative (Sect. 6.3.2.3). Negative R
2
adj can be ignored (considered as null) for the
ecological interpretation of the results.
The whole procedure of variation partitioning (except for the preliminary step of
forward selection) can be run in one R command with up to four explanatory
matrices. The function to use, available in vegan, is varpart(). Let us apply
it to the Doubs data and follow up with tests of all testable fractions.
## 1. Variation partitioning with all explanatory variables
##
(except dfs)
(spe.part.all <- varpart(spe.hel, envchem, envtopo))
plot(spe.part.all, digits = 2, bg = c("red", "blue"))
The plot gives correct values of the adjusted R squares, but the sizes of the circles
in the Venn diagram are not to scale.
This first partitioning shows that both sets of explanatory variables contribute to
the explanation of the species data. The unique contribution of the chemical variables (fraction [a], R
2
adj ¼ 0.241) is more than twice as large as that of physiography
(fraction [c], R
2
adj ¼ 0.112). The variation explained jointly by the two sets (fraction
[b], R
2
adj ¼ 0.233) is also large. This indicates that the chemical and physiographic
variables are intercorrelated. This is a good reason to make an effort towards
parsimony, and to combine variation partitioning with forward selection.
## 2. Variation partitioning after forward selection of explanatory
##
variables
# Separate forward selection in each subset of environmental
# variables
spe.chem <- rda(spe.hel, envchem)
R2a.all.chem <- RsquareAdj(spe.chem)$adj.r.squared
forward.sel(spe.hel,
envchem,
adjR2thresh = R2a.all.chem,
nperm = 9999
)
spe.topo <- rda(spe.hel, envtopo)
R2a.all.topo <- RsquareAdj(spe.topo)$adj.r.squared
forward.sel(spe.hel,
envtopo,
adjR2thresh = R2a.all.topo,
nperm = 9999
)
# Parsimonious subsets of explanatory variables, based on forward
# selections
names(envchem)
envchem.pars <- envchem[, c(4, 6, 7)]
names(envtopo)
envtopo.pars <- envtopo[, c(1, 2)]
6.3 Redundancy Analysis (RDA)
235
2 can
be negative (Sect. 6.3.2.3). Negative R
2
adj can be ignored (considered as null) for the
ecological interpretation of the results.
The whole procedure of variation partitioning (except for the preliminary step of
forward selection) can be run in one R command with up to four explanatory
matrices. The function to use, available in vegan, is varpart(). Let us apply
it to the Doubs data and follow up with tests of all testable fractions.
## 1. Variation partitioning with all explanatory variables
##
(except dfs)
(spe.part.all <- varpart(spe.hel, envchem, envtopo))
plot(spe.part.all, digits = 2, bg = c("red", "blue"))
The plot gives correct values of the adjusted R squares, but the sizes of the circles
in the Venn diagram are not to scale.
This first partitioning shows that both sets of explanatory variables contribute to
the explanation of the species data. The unique contribution of the chemical variables (fraction [a], R
2
adj ¼ 0.241) is more than twice as large as that of physiography
(fraction [c], R
2
adj ¼ 0.112). The variation explained jointly by the two sets (fraction
[b], R
2
adj ¼ 0.233) is also large. This indicates that the chemical and physiographic
variables are intercorrelated. This is a good reason to make an effort towards
parsimony, and to combine variation partitioning with forward selection.
## 2. Variation partitioning after forward selection of explanatory
##
variables
# Separate forward selection in each subset of environmental
# variables
spe.chem <- rda(spe.hel, envchem)
R2a.all.chem <- RsquareAdj(spe.chem)$adj.r.squared
forward.sel(spe.hel,
envchem,
adjR2thresh = R2a.all.chem,
nperm = 9999
)
spe.topo <- rda(spe.hel, envtopo)
R2a.all.topo <- RsquareAdj(spe.topo)$adj.r.squared
forward.sel(spe.hel,
envtopo,
adjR2thresh = R2a.all.topo,
nperm = 9999
)
# Parsimonious subsets of explanatory variables, based on forward
# selections
names(envchem)
envchem.pars <- envchem[, c(4, 6, 7)]
names(envtopo)
envtopo.pars <- envtopo[, c(1, 2)]
6.3 Redundancy Analysis (RDA)
235